Question

If $x$ and $y$ are connected parametrically by the equation,without eliminating the parameter,find $\frac{dy}{dx}.$
$x=2at^2,y=at^4$

Answer 1

The correct answer is $∴\frac{dy}{dx}=\frac{(\frac{dy}{dt})}{(\frac{dx}{dt})}=\frac{4at^3}{4at}=t^2$
The given equations are $x=2at^2,y=at^4$
Then,$\frac{dx}{dt}=\frac{d}{dt}(2at^2)=2a.\frac{d}{dt}(t^2)=2a.2t=4at$
$\frac{dy}{dt}=\frac{d}{dt}(at^4)=a.\frac{d}{dt}(t^4)=a.4.t^3=4at^3$
$∴\frac{dy}{dx}=\frac{(\frac{dy}{dt})}{(\frac{dx}{dt})}=\frac{4at^3}{4at}=t^2$